Communication networks are widely used across many industries and sections of society. Such networks may include, for example, telecommunications networks, social media networks, office networks, academia networks and community networks. The use of communication networks is growing, with continual expansion of customer bases and a steady flow of innovation providing new ways to connect and interact with other users within a network. The communication network itself provides a framework, allowing diverse groups of individuals to form connections and exchange information within the network. Connections between individual users within the network may take various forms including friendship, professional relations, common interests, shared beliefs, knowledge or backgrounds. A full service network provides a broad range of connection and communication options as well as an array of additional and value added services. Usage information may be extracted from such networks and can form the basis of personalised service offerings provided to customers according to their individual needs and interests.
There is considerable interest in being able to assess and optimise the performance of a communication network, with a view to maximising the value of the network to the network operator. The general approach to such assessment is to rank individual network customers according to their usage. However, this approach provides only limited insight to the true functioning of the network. Communication networks are often highly complex and dynamic structures within which the nature and quantity of social activity and interaction may rapidly evolve.
Another approach to assessment of communication networks is to form a graphical representation of the network, thus allowing the use of graph based algorithms and other mathematical tools. Individual users within a network may be known as nodes and referred to as vertices V on the graph, with the communication ties between nodes known as links and referred to as edges E on the graph. The network may thus be represented as a graph G (V, E) where V is the node set of n nodes and E the link set of links between the nodes. When considering a graphical representation of a typical communication network, the distribution of links can be seen to be both globally and locally inhomogeneous, with a high distribution of links within particular groups of nodes and low distribution of links between the groups. This feature of real networks is known as community structure and can be a key driver of customer behaviour within a network.
There exist various tools for attempting to analyse the local structure of graphically represented networks. These include for example the identification of small subgraphs of nodes, most notably dyads and triads. A dyad is a subgraph of two nodes and the possible links between them. A triad is a subgraph of three nodes and the possible links between them. Once identified, dyads and triads may be classified according to the number and nature of links between their constituent nodes.
The above analysis tools may be employed in attempting to enhance the performance of a communication network. For example, new connections may be suggested to users based upon usage data or an existing shared connection. However, simply introducing new connections within the network does not necessarily translate to increased traffic through the network and the speed and efficiency with which network performance may be enhanced is therefore relatively limited.